Using the ku- and BP-theoretic versions of Astey's cobordism obstruction for the existence of smooth Euclidean embeddings
of stably almost complex manifolds, we prove that, for e greater than or equal to α(n), the (2n+1)-dimensional 2e-torsion
lens space cannot be embedded in Euclidean space of dimension 4n-2α(n)+1. (Here α(n) denotes the number of ones in
the dyadic expansion of a positive integer n.) A slightly restricted version of this fact holds for e < α(n). We also
give an inductive construction of Euclidean embeddings for 2e-torsion lens spaces. Some of our best embeddings are
within one dimension of being optimal.
@article{1296138515,
author = {Gonz\'alez, Jes\'us and Landweber, Peter and Shimkus, Thomas},
title = {On the embedding dimension of 2-torsion lens spaces},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 133-160},
language = {en},
url = {http://dml.mathdoc.fr/item/1296138515}
}
González, Jesús; Landweber, Peter; Shimkus, Thomas. On the embedding dimension of 2-torsion lens spaces. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 133-160. http://gdmltest.u-ga.fr/item/1296138515/